2-0.8w=7/15w+0.2

Solution for 2-0.8w=7/15w+0.2 equation:

2-0.8w=7/15w+0.2

We move all terms to the left:

2-0.8w-(7/15w+0.2)=0


Domain of the equation: 15w+0.2)!=0

w∈R


We get rid of parentheses

-0.8w-7/15w-0.2+2=0

We multiply all the terms by the denominator


-(0.8w)*15w-(0.2)*15w+2*15w-7=0

We add all the numbers together, and all the variables

-(+0.8w)*15w-(0.2)*15w+2*15w-7=0

We multiply parentheses

-0w^2-3w+2*15w-7=0

Wy multiply elements

-0w^2-3w+30w-7=0

We add all the numbers together, and all the variables

-1w^2+27w-7=0

a = -1; b = 27; c = -7;
Δ = b2-4ac
Δ = 272-4·(-1)·(-7)
Δ = 701
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-\sqrt{701}}{2*-1}=\frac{-27-\sqrt{701}}{-2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{701}}{2*-1}=\frac{-27+\sqrt{701}}{-2}
$